Obtaining a two dimensional image of a three dimensional object is often desired, for example, for the study of organisms. Imaging of the object is often conducted via a microscope. Clarity of the image is enhanced by imaging a particular two dimensional plane, a slice, of the three dimensional object.
Conventional systems generate an image of the two dimensional plane in the three dimensional object in several different ways, including deconvolution, confocal laser scanning, and optical sectioning. For optical sectioning, conventional systems project a grid pattern onto a particular plane in the three dimensional image, and construct an image out of only those pixels in which the grid pattern falls. The plane is one selected with respect to an objective. The plane of the object to be imaged depends on the object's placement with respect to the selected plane. The grid pattern refers to a pattern of changing light intensities which can be graphed as a sine wave measured in terms of pixels, so that the peak and lowest intensities occur cyclically every given number of pixels. FIG. 1 is a diagram that illustrates components of a conventional system for performing optical sectioning, for example, a microscope. A lamp 100 emits light that is radiated onto a grid 102 of horizontal lines and that is subsequently reflected by a beam splitter 104 as the grid pattern onto the object to be imaged. Light reflected by the object, including the grid pattern, is then captured as an image by a camera 106. The image is processed by a processor 108 to generate an output image. In particular, the processor 108 provides an output image constructed of only those pixels in which the grid pattern falls.
While projecting the grid pattern onto the object allows for removal of those pixels that are not of the desired plane of the object, it also adds to the obtained image an unwanted grid pattern. Accordingly, the grid 102 is moved to multiple positions, an image is obtained at each of the positions, and the images are combined to form a single image without grid lines. A piezo-electrically driven actuator 110 is provided to move the grid 102. The piezo-electrically driven actuator 110 responds to input voltages. The voltages may be generated, for example, by the processor 108. The extent to which the piezo-electrically driven actuator 110 moves the grid 102 depends on the particular voltages applied to the piezo-electrically driven actuator 110. The particular parts of the object on which particular intensities of the grid pattern are projected depend on the position of the grid 102. The piezo-electrically driven actuator 110 is moved to move the grid between three positions. The positions are set so that the resultant intensities of corresponding grid patterns can be graphed as corresponding sine waves, where a particular point in the sine wave is phase shifted between the three grid patterns by equal phase angles, i.e., phase angles of 0 degrees, 120 degrees, and 240 degrees, each separated by 120 degrees. For each of the three positions of the grid 102, the camera 106 captures a corresponding image. FIG. 2 shows the 3 images superimposed onto each other and their corresponding grid line intensity graphs.
For each pixel, the processor 108 combines the values obtained from each of the three images using the formula IP=α√{square root over ((I1−I2)2+(I2−I3)2+(I3−I1)2)}{square root over ((I1−I2)2+(I2−I3)2+(I3−I1)2)}{square root over ((I1−I2)2+(I2−I3)2+(I3−I1)2)}, where IP represents the combined pixel value, I1, I2, and I3 each represents a pixel value for a respective one of the three images, and α equals
            2        3    .Since the grid pattern is phased by equal amounts of 120°, i.e., the phase angles are 0°, 120°, and 240°, the sine waves of the grid pattern at a particular pixel in the three images cancel each other out, i.e., their values average to zero. Further, a widefield image, i.e., the portion of the images at which the grid patterns are not in focus, are canceled out by I1−I2, I2−I3, and I3−I1. Accordingly, the value of IP determined by the combination of the three images does not include the value of the corresponding point in the grid line. The output image therefore does not include the grid lines.
In order to ensure that voltages applied to the piezo-electrically driven actuator 110 are such that cause the piezo-electrically driven actuator 110 to move the grid 102 by the correct amount, where the grid pattern is phase shifted by 120 degrees, some or all conventional systems require calibration. For calibration, an object having a substantially uniform surface, such as a smooth mirror, is inserted as the object to be imaged, and three images are captured as discussed above. If the phases are incorrect, an artefact, which is a harmonic of the grid pattern frequency, appears in the combined image. Accordingly, the voltages applied to the piezo-electrically driven actuator 110, and therefore the phases, are repeatedly changed. For each change, three images are recorded and the signal power of the artefact in the combined image is measured using a Fast Fourier Transform (FFT). The changes are repeated until the signal power is determined to be below a certain threshold, indicating substantial removal of the artefact, which corresponds to approximately correct phase shifts. Once the approximately correct phase shifts are obtained, the calibration is complete.
This procedure requires combining the pixel values of each set of three images for analysis of the artefact. The procedure typically takes 45 seconds, but can take as long as 5 minutes. Further, the phase angles are not directly determined. Instead, that which approximately corresponds to an instance where the images are at the desired phase angles, i.e., a reduction below a threshold of an artefact signal, is obtained. This procedure does not allow for accurately obtaining the desired phase angles. Further, the instance where the artefact signal is below the threshold cannot be accurately determined using FFT, in particular considering the low accuracy of FFT, which can be attributed at least in part to the measurement of the signal power in discrete values. Therefore, grid lines and/or an artefact are not completely removed from the image.
Additionally, the pixel values returned by the camera 106 are often imprecise with respect to values of image intensity. Accordingly, the measurement of the intensity of the artefact is often incorrect. The piezo-electrically driven actuator 110 is therefore incorrectly calibrated.
Furthermore, regardless of the preciseness of the calibration procedure, the output image obtained by combining the three images often includes an artefact. The artefact is often a sinusoidal variance in image intensity similar to the grid pattern. Though the sinusoidal variance of the artefact is not necessarily at a same frequency as that of the grid pattern, it is usually a product of the grid pattern and is at some harmonic of the grid pattern's sine wave. There are a number of possible causes for the artefact. An example cause is a misalignment of parts, such as the piezo-electrically driven actuator 110, which causes a change in intensities of pixel values between images (other than the intensity variance caused by the grid pattern itself). Such change in intensities results in a non-cancellation of the grid pattern of the three images when combined. Other factors may also contribute to an artefact.
Additionally, while the combination of the three images allows for the removal of grid lines, the procedure does not yield an optimal image.
Accordingly, there is a need in the art for a system and method that efficiently calibrates movement of the grid 102, and provides an optimal image without grid lines or an artefact.